Proving properties of matrix

Let A be the matrix , where no one of a,b,c,d is zero. It is required to find a non-zero 2x2 matrix X such that AX+XA=0, where 0 is the zero 2x2 matrix. Prove that either
(a) a+d=0, in which case the general solution for X depends on two parameters, or
(b) ad-bc=0, in which case the general solution for X depends on one parameter.

I don't know where to begin other than naming X= and then find the matrices AX and XA.
Thanks

Let A be the matrix , where no one of a,b,c,d is zero. It is required to find a non-zero 2x2 matrix X such that AX+XA=0, where 0 is the zero 2x2 matrix. Prove that either
(a) a+d=0, in which case the general solution for X depends on two parameters, or
(b) ad-bc=0, in which case the general solution for X depends on one parameter.

I don't know where to begin other than naming X= and then find the matrices AX and XA.
Thanks

Exactly, that's what you have to do...and then solve , where the zero in the right is, of course, the zero 2x2 matrix.